There are different ways of cooking vegetables to make them palatable. Roasting is a favorite around here, sauteeing in some butter is the other main way I make veggies. I don't steam anything... I'm not terribly fond of steamed veggies. Cauliflower is great mashed with some cream cheese, we use this as a mashed potato substitute, it's much healthier for you. But honestly if you don't like cooked veggies, there's nothing saying you have to cook them... if you like raw carrots, celery dipped in peanut butter, bell peppers with ranch (make your own), etc... there's nothing that says you can't stick to those things. A nice green salad with everything on it, sauteed mushrooms and onions served over your meat, meatballs cooked with tomato sauce. Start with what you do like and slowly try other things. It took me years and dozens of recipes to finally like brussel sprouts (but I only like them cooked one way).
Buy produce in season if at all possible. At this time of year (assuming you're in the northern hemisphere) that means apples, pears, citrus, mushrooms, peas, anything in the cabbage family (broccoli, cauliflower, brussel sprouts), potato, sweet potato, hard squash, onion, lettuce, carrots, beets, etc. If you can't find decent in-season produce, and need to buy something that is out of season (like corn in the middle of winter), buy frozen first, canned next, and fresh only as a last resort.
Read labels of anything that has one. Remove hydrogenated oils, high fructose corn syrup (also called glucose-fructose syrup), MSG and artificial sweeteners from your diet completely. Those 4 things will remove most processed foods from your diet. Avoid sugar as much as possible, use unrefined sugar (rapadura or sucanat), honey or maple syrup in your cooking if need be.
Avoid refined grains (white flour, white rice, etc.), and do some research on the proper way to prepare grains, since most people have difficulty digesting them. Don't rely on grains as the base of your diet "pyramid"... I know that the gov't has been telling us for years that we should be eating 8-12 servings a day, but that's completely unrealistic (and that's our politics at work). The majority of your diet should be fruits and vegetables, legumes, nuts, etc. That's where you'll get the most nutrition. Grains don't have nearly the nutrition profile that other edible plant matter has. You can comfortably live without grains in your life. But if you remove fruits and vegetables from your life, you'll get sick.
Don't underestimate the importance of quality. 1/2 a pound of grassfed beef has a better nutrition profile than a pound of feedlot beef. It is more expensive of course, but it is much better for you. A locally grown vegetable/fruit that was picked ripe yesterday will have more nutrition than the same item that was picked green halfway around the world and has been in transit for 5 days before it even got to the grocery store (not to even mention the difference in petro-chemical costs). Cured meats should be a last resort, not a first, as the chemicals used to keep them "fresh" are not nice to your body.
Another thing to watch out for is the over-reliance on soy products. Unfermented processed soy is not healthy, yet most people eat it half a dozen times a day. Again, read labels. Most mayonnaise that is not labeled Canola (another bad oil), is made with soy. Your "vegetable oil" is soy. Lecithin, Isoflavins and at least a dozen other ingredients are all soy.
Do some research on the importance of healthy oils, and avoid soy and canola oils. Coconut oil and olive oil are two of the best for you... if you can't afford those, go for sunflower, peanut or even corn (corn is not ideal but better than soy). I use walnut oil and safflower oil (also not ideal but better than soy) in addition to coconut oil and olive. I also keep animal fats on hand (lard, tallow, grease, etc.) that I render myself. All of those options are better for you than soy or canola oil.
You can find all sorts of information online... a great place to start is MDC's Nutrition Boards.